Abstract:   Let F be the strong p-division ring  [4].This paper is sequel to [1].Metapositive definite self-conjugate matrix over F is defined and the necessary and sufficient conditions for determining whether a partitioned matrix over F is metapositive definite self-conjugate are given.Moreover,a decomposition of pairwise matrices over F with the same numbers of columns is also presented.Whence some necessary and sufficient conditions for the existence of and the explicit expression for the metapositive definite self-conjugate solution of the matrix equation AXB=C over F are derived.

Key words: the strong p-division ring, matrix equation, metapositive definite self-conjugate matrix